代换序列,强诣零性质与混沌

本文的第一部分利用Ｍｏｒｓｅ序列研究并解决了一个代数问题，在第二部分中研究了Ｓｔｕｒｍｉａｎ系统的动力学性质，指出该系统不存在Ｌｉ－Ｙｏｒｋ意义下的混沌集。     

The degree of the E-characteristic polynomial of an even order tensor

The E-characteristic polynomial of an even order supersymmetric tensor is a useful tool in determining the positive definiteness of an even degree multivariate form. In this paper, for an even order tensor, we first establish the formula of its E-characteristic polynomial by using the classical Macaulay formula of resultants, then give an upper bound for the degree of that E-characteristic polynomial. Examples illustrate that this bound is attainable in some low order and dimensional cases.     

A Smoothing Newton Method for Semi-Infinite Programming

This paper is concerned with numerical methods for solving a semi-infinite programming problem. We reformulate the equations and nonlinear complementarity conditions of the first order optimality condition of the problem into a system of semismooth equations. By using a perturbed Fischer–Burmeister function, we develop a smoothing Newton method for solving this system of semismooth equations. An advantage of the proposed method is that at each iteration, only a system of linear equations is solved. We prove that under standard assumptions, the iterate sequence generated by the smoothing Newton method converges superlinearly/quadratically.     

Improved layer peeling algorithm for strongly reflecting fiber gratings

An improved algorithm based on the layer peeling (LP) method is proposed and demonstrated.The new method is shown to be effective for mitigating the impact of numerical errors on reconstruction of coupling function for strongly reflecting Bragg gratings.As examples,a flat-top dispersion-free fiber grating and a fiber-grating dispersion compensator are designed by the improved LP method.For a chirp grating,more accurate results are demonstrated in comparison with those obtained by the integral layer peeling (ILP) method.     

SHEAR WAVE SCATTERING FROM A PARTIALLY DEBONDED PIEZOELECTRIC CYLINDRICAL INCLUSION

I. INTRODUCTION Owing to the intrinsic coupling characteristics between electric and elastic behaviors, piezoelectricmaterials have been used widely in technology such as transducers, actuators, sensors, etc. Studieson electroelastic problems of a piezo…     

Effect of chain structure on the glass transition temperature and viscoelastic property of cis‐1,4‐polybutadiene via molecular simulation

In this work, by adopting the united atom model of cis‐1,4‐poly(butadiene) (PB), we systemically investigate the effect of the chain structure on the glass transition temperature (T_g) and the viscoelastic property of PB system. First, we analyze the atom translational mobility, bond reorientation dynamics, torsional dynamics, conformational transition rate, and dynamic heterogeneity of the PB chains with different chain structures in detail by determining the corresponding T_g. In addition, our results clearly indicate that with the decrease of the amount of the free end atoms of PB via the end‐linking method, the mobility of the PB chains quickly decreases. As a result, the T_g of the PB chains gradually increases. Depending on the chain structure and the calculation method, the T_g of the PB chains varies from 154 to 240 K. In addition, the temperature dependence of the dynamic properties has different Arrhenius behaviors above and below T_g. The calculated activation energy varies from 7.37 to 16.37 KJ/mol for different chain structures above T_g, which can be compared with those for other polymers. In addition, through the end‐linking approach the strong interaction between the PB chains improves the storage modulus G′ and the loss modulus . Meanwhile, the immobility of the free end atoms effectively reduces the friction loss of the chains under the shear field, which is reflected by the low loss factor . In summary, this work can further help to understand the effect of the chain structure on the dynamic properties of the PB chains. Meanwhile, it provides an effective approach to reduce the energy loss during the dynamic periodic deformation, which can cut the fuel consumption via the end‐linking method. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1005–1016     

Copositivity Detection of Tensors: Theory and Algorithm

A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositive tensors have found important applications in polynomial optimization, tensor complementarity problems and vacuum stability of a general scalar potential. In this paper, we consider copositivity detection of tensors from both theoretical and computational points of view. After giving several necessary conditions for copositive tensors, we propose several new criteria for copositive tensors based on the representation of the multivariate form in barycentric coordinates with respect to the standard simplex and simplicial partitions. It is verified that, as the partition gets finer and finer, the concerned conditions eventually capture all strictly copositive tensors. Based on the obtained theoretical results with the help of simplicial partitions, we propose a numerical method to judge whether a tensor is copositive or not. The preliminary numerical results confirm our theoretical findings.     

带空间机械臂航天器姿态运动规划的数值算法研究

自由漂浮空间机械臂系统在无外力矩作用时,系统的动量矩守恒而成为非完整系统。利用这一特性本文研究了自由漂浮空间机械臂系统的三维姿态运动规划问题。导出带空间机械臂的航天器三维姿态运动数学模型,将系统的非完整运动规划问题转化为非线性系统最优控制问题,在最优控制中利用小波逼近控制输入规律,提出基于遗传算法的最优控制数值算法。通过数值仿真,表明该方法对带空间机械臂航天器系统的非完整姿态运动规划是有效的。     

Polymer-nanoparticle interfacial behavior revisited: a molecular dynamics study

By tuning the polymer-filler interaction, filler size and filler loading, we use a coarse-grained model-based molecular dynamics simulation to study the polymer-filler interfacial structural (the orientations at the bond, segment and chain length scales, chain size and conformation), dynamic and stress-strain properties. Simulated results indicate that the interfacial region is composed of partial segments of different polymer chains, which is consistent with the experimental results presented by Chen et al. (Macromolecules, 2010, 43, 1076). Moreover, it is found that the interfacial region is within one single chain size (R(g)) range, irrespective of the polymer-filler interaction and the filler size, beyond which the bulk behavior appears. In the interfacial region, the orientation and dynamic behaviors are induced by the interfacial enthalpy, while the size and conformation of polymer chains near the filler are controlled by the configurational entropy. In the case of strong polymer-filler interaction (equivalent to the hydrogen bond), the innerest adsorbed polymer segments still undergo adsorption-desorption process, the transport of chain mass center in the interfacial region exhibits away from the glassy behavior, and no plastic-like yielding point appears in the stress-strain curve, which indicates that although the mobility of interfacial polymer chains is restricted, there exist no "polymer glassy layers" surrounding the filler. In addition, it is evidenced that the filler particle prefers selectively adsorbing the long polymer chains for attractive polymer-filler interaction, validating the experimental explanation of the change of the bound rubber (BR). In short, this work provides important information for further experimental and simulation studies of polymer-nanoparticle interfacial behavior.